Is it permissible to listen to chants praising the Prophet if accompanied by musical instruments?
If singing, or chanting in praise of the Prophet was accompanied by a forbidden musical instrument, then it is forbidden.
Has Islam made it incumbent on us to give our children particular names?
No, it hasn`t, but it is desirable that we give them good names.
Is it permissible to make up missed prayers at the times in which praying is disliked?
All perfect praise be to Allah,The Lord of The Worlds It is permissible to make up missed prayers at any time even that in which praying is disliked. Absolute supererogatory prayer is forbidden to be performed at the times in which praying is disliked, and this also applies to Ihram and Istikhara prayers. However, there is no harm in offering prayers in Mekah during those times. And Allah Knows Best.
Is it permissible to offer Salah (prayer) on behalf of the sick who is on his/her death bed, and is incapable of offering it?
It`s impermissible to offer Salah on behalf of the sick, or the dead.